Chaotic Neural Networks with a Random Topology Can Achieve Pattern Recognition
Ke Qin, B. John Oommen · 2013
This paper conrms the fascinating result that we can design chaotic Neural Networks (NNs) that have a random topology and that these NNs can achieve chaotic Pattern Recognition (PR). What we imply by this is that the NN yields a strong periodic or more frequent signal when a pattern is recognized, and in between two consecutively recognized patterns, none of the trained patterns are recalled. Finally, and most impor- tantly, if an untrained pattern is presented, the system yields a chaotic signal. The basic model that we use here is the Adachi Neural Network (AdNN), which we modify in a random manner. The AdNN is a fascinating NN which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and PR, and some of its variants have also been used to obtain other PR phenomena, including blurring. All these NNs require a quadratic number of computations in the training phase. This computa- tion was reduced to be linear in (1) by resorting to a Maximum Spanning Tree topology, and a gradient search method. In this paper, we mainly consider the issue of how the network topology can be modied by involving randomized connections so as to render the new network much closer to \real NNs. At the same time, we require that the newly obtained network still displays PR characteristics. To achieve this, we rst construct a random network by means of the E-R model and then address the problem of computing the weights for the new network. This is done by constraining the the modied random connection-based NN to have approximately the same input-output characteristics using a gradient-based algorithm. Through a detailed experimental analysis, we show that the new random AdNN-like network possesses PR properties for appropriate settings. As far as we know, such a random AdNN has not been reported, and our present results are novel.